Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Some Diffusion Models for the Mabinogion Sheep Problem of Williams

Terence Chan
Advances in Applied Probability
Vol. 28, No. 3 (Sep., 1996), pp. 763-783
DOI: 10.2307/1428180
Stable URL: http://www.jstor.org/stable/1428180
Page Count: 21
  • Read Online (Free)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Some Diffusion Models for the Mabinogion Sheep Problem of Williams
Preview not available

Abstract

The 'Mabinogion sheep' problem, originally due to D. Williams, is a nice illustration in discrete time of the martingale optimality principle and the use of local time in stochastic control. The use of singular controls involving local time is even more strikingly highlighted in the context of continuous time. This paper considers a class of diffusion versions of the discrete-time Mabinogion sheep problem. The stochastic version of the Bellman dynamic programming approach leads to a free boundary problem in each case. The most surprising feature in the continuous-time context is the existence of diffusion versions of the original discrete-time problem for which the optimal boundary is different from that in the discrete-time case; even when the optimal boundary is the same, the value functions can be very different.

Page Thumbnails

  • Thumbnail: Page 
763
    763
  • Thumbnail: Page 
764
    764
  • Thumbnail: Page 
765
    765
  • Thumbnail: Page 
766
    766
  • Thumbnail: Page 
767
    767
  • Thumbnail: Page 
768
    768
  • Thumbnail: Page 
769
    769
  • Thumbnail: Page 
770
    770
  • Thumbnail: Page 
771
    771
  • Thumbnail: Page 
772
    772
  • Thumbnail: Page 
773
    773
  • Thumbnail: Page 
774
    774
  • Thumbnail: Page 
775
    775
  • Thumbnail: Page 
776
    776
  • Thumbnail: Page 
777
    777
  • Thumbnail: Page 
778
    778
  • Thumbnail: Page 
779
    779
  • Thumbnail: Page 
780
    780
  • Thumbnail: Page 
781
    781
  • Thumbnail: Page 
782
    782
  • Thumbnail: Page 
783
    783